2 % (c) The GRASP/AQUA Project, Glasgow University, 1998
4 \section[TypeRep]{Type - friends' interface}
8 Type(..), TyNote(..), -- Representation visible
9 SourceType(..), -- to friends
11 Kind, PredType, ThetaType, -- Synonyms
14 superKind, superBoxity, -- KX and BX respectively
15 liftedBoxity, unliftedBoxity, -- :: BX
17 typeCon, -- :: BX -> KX
18 liftedTypeKind, unliftedTypeKind, openTypeKind, -- :: KX
19 mkArrowKind, mkArrowKinds, -- :: KX -> KX -> KX
21 usageKindCon, -- :: KX
22 usageTypeKind, -- :: KX
23 usOnceTyCon, usManyTyCon, -- :: $
24 usOnce, usMany, -- :: $
29 #include "HsVersions.h"
33 import VarEnv ( TyVarEnv )
34 import VarSet ( TyVarSet )
36 import BasicTypes ( IPName )
37 import TyCon ( TyCon, KindCon, mkFunTyCon, mkKindCon, mkSuperKindCon )
38 import Class ( Class )
41 import PrelNames ( superKindName, superBoxityName, liftedConName,
42 unliftedConName, typeConName, openKindConName,
43 usageKindConName, usOnceTyConName, usManyTyConName,
48 %************************************************************************
50 \subsection{Type Classifications}
52 %************************************************************************
56 *unboxed* iff its representation is other than a pointer
57 Unboxed types are also unlifted.
59 *lifted* A type is lifted iff it has bottom as an element.
60 Closures always have lifted types: i.e. any
61 let-bound identifier in Core must have a lifted
62 type. Operationally, a lifted object is one that
65 Only lifted types may be unified with a type variable.
67 *algebraic* A type with one or more constructors, whether declared
68 with "data" or "newtype".
69 An algebraic type is one that can be deconstructed
70 with a case expression.
71 *NOT* the same as lifted types, because we also
72 include unboxed tuples in this classification.
74 *data* A type declared with "data". Also boxed tuples.
76 *primitive* iff it is a built-in type that can't be expressed
79 Currently, all primitive types are unlifted, but that's not necessarily
80 the case. (E.g. Int could be primitive.)
82 Some primitive types are unboxed, such as Int#, whereas some are boxed
83 but unlifted (such as ByteArray#). The only primitive types that we
84 classify as algebraic are the unboxed tuples.
86 examples of type classifications:
88 Type primitive boxed lifted algebraic
89 -----------------------------------------------------------------------------
91 ByteArray# Yes Yes No No
92 (# a, b #) Yes No No Yes
93 ( a, b ) No Yes Yes Yes
98 ----------------------
100 ----------------------
105 Then we want N to be represented as an Int, and that's what we arrange.
106 The front end of the compiler [TcType.lhs] treats N as opaque,
107 the back end treats it as transparent [Type.lhs].
109 There's a bit of a problem with recursive newtypes
111 newtype Q = MkQ (Q->Q)
113 Here the 'implicit expansion' we get from treating P and Q as transparent
114 would give rise to infinite types, which in turn makes eqType diverge.
115 Similarly splitForAllTys and splitFunTys can get into a loop.
117 Solution: for recursive newtypes use a coerce, and treat the newtype
118 and its representation as distinct right through the compiler. That's
119 what you get if you use recursive newtypes. (They are rare, so who
120 cares if they are a tiny bit less efficient.)
122 So: non-recursive newtypes are represented using a SourceTy (see below)
123 recursive newtypes are represented using a TyConApp
125 The TyCon still says "I'm a newtype", but we do not represent the
126 newtype application as a SourceType; instead as a TyConApp.
129 %************************************************************************
131 \subsection{The data type}
133 %************************************************************************
137 type SuperKind = Type
140 type TyVarSubst = TyVarEnv Type
146 Type -- Function is *not* a TyConApp
149 | TyConApp -- Application of a TyCon
150 TyCon -- *Invariant* saturated appliations of FunTyCon and
151 -- synonyms have their own constructors, below.
152 [Type] -- Might not be saturated.
154 | FunTy -- Special case of TyConApp: TyConApp FunTyCon [t1,t2]
158 | ForAllTy -- A polymorphic type
162 | SourceTy -- A high level source type
163 SourceType -- ...can be expanded to a representation type...
165 | NoteTy -- A type with a note attached
167 Type -- The expanded version
170 = FTVNote TyVarSet -- The free type variables of the noted expression
172 | SynNote Type -- Used for type synonyms
173 -- The Type is always a TyConApp, and is the un-expanded form.
174 -- The type to which the note is attached is the expanded form.
177 -------------------------------------
182 represents a value whose type is the Haskell source type sty.
183 It can be expanded into its representation, but:
185 * The type checker must treat it as opaque
186 * The rest of the compiler treats it as transparent
188 There are two main uses
189 a) Haskell predicates
192 Consider these examples:
193 f :: (Eq a) => a -> Int
194 g :: (?x :: Int -> Int) => a -> Int
195 h :: (r\l) => {r} => {l::Int | r}
197 Here the "Eq a" and "?x :: Int -> Int" and "r\l" are all called *predicates*
198 Predicates are represented inside GHC by PredType:
202 = ClassP Class [Type] -- Class predicate
203 | IParam (IPName Name) Type -- Implicit parameter
204 | NType TyCon [Type] -- A *saturated*, *non-recursive* newtype application
205 -- [See notes at top about newtypes]
207 type PredType = SourceType -- A subtype for predicates
208 type ThetaType = [PredType]
211 (We don't support TREX records yet, but the setup is designed
212 to expand to allow them.)
214 A Haskell qualified type, such as that for f,g,h above, is
216 * a FunTy for the double arrow
217 * with a PredTy as the function argument
219 The predicate really does turn into a real extra argument to the
220 function. If the argument has type (PredTy p) then the predicate p is
221 represented by evidence (a dictionary, for example, of type (predRepTy p).
224 %************************************************************************
228 %************************************************************************
232 kind :: KX = kind -> kind
234 | Type liftedness -- (Type *) is printed as just *
235 -- (Type #) is printed as just #
237 | UsageKind -- Printed '$'; used for usage annotations
239 | OpenKind -- Can be lifted or unlifted
242 | kv -- A kind variable; *only* happens during kind checking
244 boxity :: BX = * -- Lifted
246 | bv -- A boxity variable; *only* happens during kind checking
248 There's a little subtyping at the kind level:
249 forall b. Type b <: OpenKind
251 That is, a type of kind (Type b) is OK in a context requiring an OpenKind
253 OpenKind, written '?', is used as the kind for certain type variables,
256 1. The universally quantified type variable(s) for special built-in
257 things like error :: forall (a::?). String -> a.
258 Here, the 'a' can be instantiated to a lifted or unlifted type.
260 2. Kind '?' is also used when the typechecker needs to create a fresh
261 type variable, one that may very well later be unified with a type.
262 For example, suppose f::a, and we see an application (f x). Then a
263 must be a function type, so we unify a with (b->c). But what kind
264 are b and c? They can be lifted or unlifted types, or indeed type schemes,
265 so we give them kind '?'.
267 When the type checker generalises over a bunch of type variables, it
268 makes any that still have kind '?' into kind '*'. So kind '?' is never
269 present in an inferred type.
272 ------------------------------------------
273 Define KX, the type of a kind
274 BX, the type of a boxity
277 superKind :: SuperKind -- KX, the type of all kinds
278 superKind = TyConApp (mkSuperKindCon superKindName) []
280 superBoxity :: SuperKind -- BX, the type of all boxities
281 superBoxity = TyConApp (mkSuperKindCon superBoxityName) []
284 ------------------------------------------
285 Define boxities: @*@ and @#@
288 liftedBoxity, unliftedBoxity :: Kind -- :: BX
289 liftedBoxity = TyConApp (mkKindCon liftedConName superBoxity) []
291 unliftedBoxity = TyConApp (mkKindCon unliftedConName superBoxity) []
294 ------------------------------------------
295 Define kinds: Type, Type *, Type #, OpenKind, and UsageKind
298 typeCon :: KindCon -- :: BX -> KX
299 typeCon = mkKindCon typeConName (superBoxity `FunTy` superKind)
301 liftedTypeKind, unliftedTypeKind, openTypeKind :: Kind -- Of superkind superKind
303 liftedTypeKind = TyConApp typeCon [liftedBoxity]
304 unliftedTypeKind = TyConApp typeCon [unliftedBoxity]
306 openKindCon = mkKindCon openKindConName superKind
307 openTypeKind = TyConApp openKindCon []
309 usageKindCon = mkKindCon usageKindConName superKind
310 usageTypeKind = TyConApp usageKindCon []
313 ------------------------------------------
317 mkArrowKind :: Kind -> Kind -> Kind
318 mkArrowKind k1 k2 = k1 `FunTy` k2
320 mkArrowKinds :: [Kind] -> Kind -> Kind
321 mkArrowKinds arg_kinds result_kind = foldr mkArrowKind result_kind arg_kinds
325 %************************************************************************
327 \subsection{Wired-in type constructors
329 %************************************************************************
331 We define a few wired-in type constructors here to avoid module knots
334 funTyCon = mkFunTyCon funTyConName (mkArrowKinds [liftedTypeKind, liftedTypeKind] liftedTypeKind)
337 ------------------------------------------
338 Usage tycons @.@ and @!@
340 The usage tycons are of kind usageTypeKind (`$'). The types contain
341 no values, and are used purely for usage annotation.
344 usOnceTyCon = mkKindCon usOnceTyConName usageTypeKind
345 usOnce = TyConApp usOnceTyCon []
347 usManyTyCon = mkKindCon usManyTyConName usageTypeKind
348 usMany = TyConApp usManyTyCon []